text: To Find Horizontal Asymptotes: 1) Put equation or function in y= form. 2) Multiply out (expand) any factored polynomials in the numerator or denominator. 3) Remove everything except the terms with the biggest exponents of x found in the numerator and denominator. These are the dominant terms.Sample A: Find the horizontal asymptotes of: Remember that horizontal asymptotes appear as x extends to positive or negative infinity, so we need to figure out what this fraction approaches as x gets huge. To do that, we'll pick the dominant terms in the numerator and denominator.hese are the dominant terms. Sample A: Find the horizontal asymptotes of: Remember that horizontal asymptotes appear as x extends to positive or negative infinity, so we need to figure out what this fraction approaches as x gets huge. To do that, we'll pick the dominant terms in the numerator and denominator.